In the seventies, Rosenbrock [1]} introduced the concept of a polynomial system matrix \(L(\lambda )\)  of an arbitrary rational matrix \(R(\lambda )\in \mathbb {C}(\lambda )^{m\times n}\) .
Such a system matrix is partitioned in a quadruple \(\lbrace A(\lambda ),B(\lambda ),C(\lambda ),D(\lambda )\rbrace \)  of compatible polynomial matrices
\(  L(\lambda ):=\left[\begin{array}{ccc} A(\lambda ) & -B(\lambda ) \\ C(\lambda ) & D(\lambda )\end{array}\right]\) 
